Bevel modifier stops to work for diagonal faces
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There are a couple of things to try here.

First, select everything in edit mode and press ShiftN to recalculate the normals. Sometimes Blender gets the direction the vertices are facing confused, and this causes issue with beveling.

Second, try and get rid of the 'ngons', aka faces with more than 4 vertices. Beveling ngons is always a bit risky, and when you start moving things around it's not uncommon to see issues pop up. Insetting the ngons with I is a possible way to get some nice quads along the edge of your bevel.